Kinematic formulas for integral invariants of degree two in real space forms Hong KangTakashi SakaiYoung Suh 53C53C65integral geometrykinematic formulareal space formsecond fundamental formmean curvaturehomogeneous polynomial In this paper we investigate the kinematic formulas for submanifolds in real space forms, and we give explicit expressions of the kinematic formulas for integral invariants defined by invariant homogeneous polynomials of degree two on second fundamental forms in the sense of Howard, completely. They are actually certain extensions of the Chern-Federer kinematic formula and of the one by Chen. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2582 10.1512/iumj.2005.54.2582 en Indiana Univ. Math. J. 54 (2005) 1499 - 1520 state-of-the-art mathematics http://iumj.org/access/